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Factor analysis is a statistical method for explaining the variation of a large number of observed, correlated variables using a smaller number of unobserved, latent variables (factors). It is closely related to principal component analysis (PCA) and represents one of the most well-known latent variable models. Although PCA determines the components using standard geometrical procedures and is mostly exploratory, factor analysis can be either exploratory or confirmatory. Exploratory factor analysis assumes that any latent factor can be associated with any observed variable (described by the factor loadings) and is suitable for revealing the underlying structure of relatively large data sets. Confirmatory factor analysis is more subjective, where researchers usually have strong prior belief on the number of latent factors as well as the potential variables associated with each factor. Bayesian sparse factor modeling was first introduced by Mike West for the analysis of microarray gene expression profiles (West, 2003) and was later applied to a diverse range of bioinformatics studies including the inference of transcriptional regulatory networks (Sabatti et al., 2005), biological pathway analysis (Carvalho et al., 2008), population structure analysis (Engelhardt and Stephens, 2010), and other areas. In this chapter, we first introduce classical factor analysis models and Bayesian sparse factor analysis models and associated inferential methods. We then review several applications of this general approach in computational biology. This chapter ends with discussion on future developments.
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